Question

Year return (HPY) of C return (HPY) of F

2016 −18.00% −14.50%

2017 33.00% 21.80%

2018 15.00 % 30.50%

2019 −0.50% −7.60%

2020 27.00% 26.30%

Required

Calculate the geometric rate of return for each stock during the 5-year period. (6mks)

Calculate the standard deviation of returns for each stock. (10mks)

Calculate the coefficient of variation for each stock. (2mks)

If you are a risk-averse investor then, assuming these are your only choices, discuss whether you would prefer to hold Stock C or Stock F. (2mks)

Answer 1

geometric rate of return for each stock:

$GAR=((1+r1)*(1+r1)*...(1+rn))^\frac{1}{5})-1$

$GAR(C)=((1+r1)*(1+r1)*...(1+rn))^\frac{1}{5})-1=18.16$

$GAR(F)=((1+r1)*(1+r1)*...(1+rn))^\frac{1}{5})-1=19.85$

$\sigma=(\frac{\Sigma(x-\bar{x})}{n})^\frac{1}{2}$

$\sigma(c)=(\frac{\Sigma(x-\bar{x})}{n})^\frac{1}{2}=11.2$

$\sigma(F)=(\frac{\Sigma(x-\bar{x})}{n})^\frac{1}{2}=8.21$

$Var=\frac{\sigma}{\bar{x}}$

$Var (C)=\frac{\sigma}{\bar{x}}=59.49$

$Var (F)=\frac{\sigma}{\bar{x}}=40.77$

The higher the coefficient of variation, the higher the risk is considered, so securities are preferred F